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Títol: Transverse intersections between invariant manifolds of doubly hyperbolic invariant tori, via the Poincaré-Mel'nikov method
Autor: Gutiérrez Serrés, Pere
Delshams Valdés, Amadeu
Pacha Andújar, Juan Ramón
Altres autors/autores: Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
Matèries: Àrees temàtiques de la UPC::Matemàtiques i estadística
Equacions diferencials ordinàries
Hamilton, Sistemes de
Tipus de document: External research report
Descripció: We consider a perturbation of an integrable Hamiltonian system having an equilibrium point of elliptic-hyperbolic type, having a homoclinic orbit. More precisely, we consider an (n+2)-degree-of-freedom near integrable Hamiltonian with n centres and 2 saddles, and assume that the homoclinic orbit is preserved under the perturbation. On the centre manifold near the equilibrium, there is a Cantorian family of hyperbolic KAM tori, and we study the homoclinic intersections between the stable and unstable manifolds associated to such tori. We establish that, in general, the manifolds intersect along transverse homoclinic orbits. In a more concrete model, such homoclinic orbits can be detected, in a first approximation, from nondegenerate critical points of a Mel'nikov potential. We provide bounds for the number of transverse homoclinic orbits using that, in general, the potential will be a Morse function (which gives a lower bound# and can be approximated by a trigonometric polynomial #which gives an upper bound)
Altres identificadors i accés: http://hdl.handle.net/2117/7156
Disponible al dipòsit:E-prints UPC
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